
where \(\omega _V = \sqrt{{\mathbf {k}}^2 + M_V^2}\)  and \(\mu \)  is the QCD renormalization scale.
The above result is in agreement with estimates of the pion electromagnetic mass splitting [1]}, [2]}, [3]}, [4]}, [5]}.
Taking \(M_V = 775\,\text{MeV}\) , \(F_\pi = 92.28\,\text{MeV}\) ,
and \({g}_{LR}^{\pi \pi }=8.23\)  from lattice QCD [6]},
the sum of low- and high-momentum components \(Z^<(\Lambda ) + Z^> (\Lambda )\)  equals 0.63 at \(\Lambda = 2\,\text{GeV}\) 
and reaches the asymptotic value \(Z^< (\Lambda \rightarrow \infty )= 0.67\) .
The deficit compared to the experimental value \(Z \simeq 0.8\)  is understood in terms of
the neglected inelastic contributions from the axial-vector resonances [1]}, [2]}, [3]}, thus providing another estimate of the error due to neglecting inelastic corrections.
